The influence of orthogonality on the Arnoldi method
type: Item
instance of: scholarly article
title: The influence of orthogonality on the Arnoldi method
zbMATH Open document ID: 0948.65034
DOI: 10.1016/S0024-3795(99)00100-7
author: Yanyan Li
published in: Linear Algebra and its Applications
publication date: 2000-11-13T00:00:00Z
review text: Error bounds for five orthogonalization methods and the Arnoldi method are summarized. It is shown that quality of the eigensolvers depends on the orthonormality of the computed basis. It is also shown that the stopping criterion based on the backward error and the value computed using the Arnoldi method can differ because of the loss of orthonormality of the computed basis of the Krylov subspace. A bound that quantifies this difference is given. Results of some computational experiments are also given.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F25
zbMATH DE Number: 1443454
zbMATH Keywords: orthonormal basis
zbMATH Keywords: QR factorization
zbMATH Keywords: Arnoldi method
zbMATH Keywords: Krylov subspace method
zbMATH Keywords: numerical examples
zbMATH Keywords: eigenvalues
zbMATH Keywords: error bounds
zbMATH Keywords: orthogonalization methods
reviewed by: R. P. Tewarson
describes a project that uses: mctoolbox
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1443454